1/4x+3=-5x

Solution for 1/4x+3=-5x equation:

1/4x+3=-5x

We move all terms to the left:

1/4x+3-(-5x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x+5x+3=0

We multiply all the terms by the denominator


5x*4x+3*4x+1=0

Wy multiply elements

20x^2+12x+1=0

a = 20; b = 12; c = +1;
Δ = b2-4ac
Δ = 122-4·20·1
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8}{2*20}=\frac{-20}{40}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8}{2*20}=\frac{-4}{40}
=-1/10
$